The use of capacitors with temperature dependent dielectric constants to convert heat to electric energy is well known. Representative devices that use dielectrics as variable capacitors to generate electricity are disclosed, for example, in U.S. Pat. No. 4,220,906 to Drummond, U.S. Pat. Nos. 4,425,540 and 4,647,836 to Olsen, U.S. Pat. No. 6,528,898 to Ikura et al. and U.S. Pat. No. 7,323,506 to Kouchachvili et al. Those devices simply utilize the fact that the dielectric constant of certain materials, such as ferroelectrics, varies as temperature varies. Specifically, those devices use the dielectrics as temperature dependent variable capacitors, the capacitance of which decreases as the temperature is increased by the absorption of heat. The capacitor is partially charged under an applied field at the lower temperature, and is then fully charged by increasing the electric field. The capacitor is then heated while under that large field, and it partially discharges as the dielectric constant decreases with increasing temperature and correspondingly decreasing capacitance. Further discharge occurs by reducing the applied field while the capacitor remains at high temperature. (U.S. Pat. No. 4,425,540 to Olsen). Such cycling of the temperature and dielectric constant of a capacitor under an applied field is referred to as the Olsen cycle.
The physics of the capacitor device is straightforward. The voltage V of a capacitor of capacitance C is inversely proportional to the dielectric constant ∈:V=Q/C=Q/[∈(T)∈0(A/d)].After the capacitor has been fully charged by application of the external field under the Olsen cycle, the capacitor is heated to a temperature at which the dielectric constant, ∈, decreases. During that heating step of the Olsen cycle, partial discharge occurs because the charge, Q, held by the capacitor decreases while V is held constant.
The use of dielectrics as variable capacitors to generate electricity is also reported by Olsen in Cascaded Pyroelectric Converter, 59 FERROELECTRICS 205 (1984). Olsen reports a maximum power density of 33 W/L (about 4 W/kg) using the ferroelectric PZST as the dielectric material in a variable capacitor device with multiple stages and regeneration. Using finite element simulation, Vanderpool calculates that the Olsen cycle yields a power density of 24 W/L (about 3 W/kg) under certain conditions using PZST as the dielectric material in a variable capacitor. Vanderpool, Simulations of a Prototypical Device Using Pyroelectric Materials for Harvesting Waste Heat, 51 INT. J. HT & MASS TRANSFER 5051 (2008).
The variable capacitor method of converting heat to electricity is not the most effective method of using ferroelectrics to generate electricity, however. True pyroelectric generation focuses, instead, on the inherent polarization that occurs spontaneously in the ferroelectric phase, independent of polarization induced by an applied field. That inherent polarization provides a much more robust source of electric energy. Variable capacitors do not use the powerful inherent spontaneous polarization that occurs in ferroelectrics without an applied field. Further, the application of large external fields and the continuous application of an external field during cycling impede the more powerful energy conversion that can be achieved with ferroelectrics through spontaneous polarization. Such external fields prevent the effective use of the tremendous electrical energy that arises from the electric dipoles of ferroelectric materials spontaneously and without induction by an external field.
Apparatus and methods for using the inherent spontaneous polarization of ferroelectrics to convert heat-to-electricity are disclosed in U.S. patent application Ser. No. 12/465,924 and U.S. Pat. No. 7,982,360 to Erbil. The inventions presented there, unlike the prior art, utilize the spontaneous polarization of ferroelectrics, together with the rapid change in spontaneous polarization that occurs during phase transition, to convert heat-to-electrical energy. Unlike the variable capacitor approach, those inventions do not rely on the application of an electric field to induce electric dipoles in the ferroelectric material. They do contemplate the use of a small electric field during or after transition to the ferroelectric phase in order to pole the ferroelectric, but that field is not used to create the fundamental polarization in the unit cells themselves. The poling field simply aligns the inherent electric dipoles that occur spontaneously when the material is at a temperature that causes it to be in its ferroelectric phase.
The apparatus and methods set forth in application Ser. No. 12/465,924 and U.S. Pat. No. 7,982,360 are a new way of converting thermal energy to electricity. With that new methodology, there exists a need to address optimal ways to use spontaneous polarization for the purpose of generating electricity from thermal energy.